Cricket latest: Bairstow revives Yorkshire at Scarborough
Bairstow is unbeaten on 80 as Yorkshire went into tea on 207-4.
After resuming on 84-3 after lunch, Yorkshire lost only one wicket during the afternoon session - that of captain Andrew Gale.
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Hide AdGale had made 80 when he drove loosely at a wide delivery from Wayne White and was caught behind after sharing in a fourth-wicket stand of 160 with Bairstow in 41 overs.
The pair brought respectability to the Yorkshire scorecard after the home team slipped to 33-3 in the morning session.
They matched each other blow for blow against a Leicestershire side who have not helped their cause with four dropped catches.
The other not out batsman at the break is Gary Ballance, who has eight runs to his name.
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Hide AdYorkshire: Root, Sayers, Jaques, Gale (captain), Bairstow, Ballance, McGrath, Bresnan, Rashid, Sidebottom, Patterson.
Leicestershire: Boyce, Smith, du Toit, Sarwan (captain), Cobb, Eckersley, White, Joseph, Malik, Wyatt, Henderson.